using the identity to evaluate a sum

so I have 1/2( k=1 to n 1/(k-1)-1/(k+1)). I feel like from here i'm supposed to manipulate the 1/k-1 to some how get it so I can have a_j =1/(j+1) and then replace all the 1/k+1 by a_j..however i'm not exactly sure how to go about this. Would it turn into 1/a_j-2 -a_j ?? if so what do i do from here?

First of all, your sum can't possibly start with because it gives a denominator, so I assume you mean for it to start at .
Second, it really helps to use LaTeX so that everyone can read what you are writing.

Hey thanks so much! It was soooo much easier to see when you expand everything out..i don't know why i didn't even bother to expand it but thanks. Oh and i'm sorry for my lack of latex skill, i am trying to use them and i keep referring to a latex table but i seem to be horrible at applying them correctly. I need more practice with it and i will def work on it! i'm sorry it was so hard to read but thank you for clearing it up for everyone to see. (and also i did mean k=2 thats what i have on my scrap paper my bad). Thanks again.